A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60° with the horizontal (see the figure). Approximate the height of the kite above level ground if 700 feet of string is payed out. (Round your answer to one decimal place.)

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that is 30.0 meters from the base of the antenna. If the wire makes an angle of 55°10' with the ground, approximate the length l of the wire. (Round your answer to the nearest tenth.)

A rocket is fired at sea level and climbs at a constant angle of 65° through a distance of 20,000 feet. Approximate its altitude to the nearest foot.
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To solve these problems, we can use trigonometric functions such as sine, cosine, and tangent.

For the first problem:
1. Draw a diagram with the ground level, the height of the kite, and the angle made with the horizontal.
2. Since the string of the kite is taut, it forms a right triangle with the ground.
3. The angle made with the horizontal is given as 60°, so the angle made with the ground is 90° - 60° = 30°.
4. We are given the length of the string as 700 feet and need to find the height of the kite.
5. The sine function relates the opposite side (the height of the kite) to the hypotenuse (the length of the string). So, we can use the sine function: sin(30°) = height / 700.
6. Rearranging the equation, we get: height = 700 * sin(30°).
7. Calculate the approximate height using a scientific calculator or trigonometric tables. The result will be in feet.

For the second problem:
1. Draw a diagram with the radio antenna, the horizontal ground, and the angle made with the ground.
2. We are given the distance from the base of the antenna to the point where the wire is attached as 30.0 meters and need to find the length of the wire.
3. The given angle is in degrees and minutes. Convert it to decimal degrees by adding the decimal value of the minutes: 55°10' = 55 + (10/60) = 55.167°.
4. The wire forms a right triangle with the ground, and we need to find the hypotenuse (the length of the wire).
5. The cosine function relates the adjacent side (the distance from the base of the antenna) to the hypotenuse. So, we can use the cosine function: cos(55.167°) = distance / length.
6. Rearranging the equation, we get: length = distance / cos(55.167°).
7. Calculate the approximate length using a scientific calculator or trigonometric tables. The result will be in meters.

For the third problem:
1. Draw a diagram with the rocket, the sea level, and the angle of climb.
2. We are given the distance climbed as 20,000 feet and need to find the altitude.
3. The distance climbed forms the opposite side of the right triangle, and we need to find the hypotenuse (the altitude).
4. The sine function relates the opposite side to the hypotenuse. So, we can use the sine function: sin(65°) = altitude / 20,000.
5. Rearranging the equation, we get: altitude = 20,000 * sin(65°).
6. Calculate the approximate altitude using a scientific calculator or trigonometric tables. The result will be in feet.

Remember to round your answers to the specified decimal places or nearest tenth as mentioned in the problem.